MATLAB Implementation of Gabor Transform with Code Description

The Gabor transform serves as a classical time-frequency analysis method capable of providing precise signal characterization simultaneously in both time and frequency domains. Its fundamental principle involves performing localized spectral analysis using a set of modulated Gaussian window functions, making it particularly suitable for processing non-stationary signals. In MATLAB implementation, the Gabor transform typically involves the following key steps: First, designing a bank of Gabor filters composed of Gaussian functions multiplied by sinusoids at different scales and orientations. The frequency selectivity of these filters can be controlled by adjusting center frequency and bandwidth parameters. The implementation then performs point-by-point sliding window analysis, where the input signal is convolved with each Gabor filter to obtain coefficient distributions across the time-frequency plane. A standard MATLAB implementation includes three main modules: parameter initialization, filter generation, and signal decomposition. The filter generation module requires special attention to constructing complex-valued Gabor kernel functions, typically implemented using MATLAB's array operations and complex number support. The signal processing module must address boundary effect issues, which can be handled using symmetric padding or circular extension techniques. The visualization of time-frequency spectrograms enables intuitive observation of how signal frequency components evolve over time, achieved through MATLAB's image or surface plotting functions like imagesc() or surf(). This implementation finds significant applications in speech analysis, texture recognition, and other domains, with its main advantage being superior time-frequency resolution balance compared to STFT. For practical engineering applications, computational efficiency optimization should be considered, such as accelerating convolution operations through FFT implementation using MATLAB's fftconv() or custom FFT-based convolution algorithms.